Computing Nash equilibria and evolutionarily stable states of evolutionary games

Stability analysis is an important research direction in evolutionary game theory. Evolutionarily stable states have a close relationship with Nash equilibria of repeated games, which are characterized by the folk theorem. When applying the folk theorem, one needs to compute the minimax profile of the game in order to find Nash equilibria. Computing the minimax profile is an NP-hard problem. In this paper we investigate a new methodology to compute evolutionary stable states based on the level-k equilibrium, a new refinement of Nash equilibrium in repeated games. A level-k equilibrium is implemented by a group of players who adopt reactive strategies and who have no incentive to deviate from their strategies simultaneously. Computing the level-k equilibria is tractable because the minimax payoffs and strategies are not needed. As an application, this paper develops a tractable algorithm to compute the evolutionarily stable states and the Pareto front of n-player symmetric games. Three games, including the iterated prisoner’s dilemma, are analyzed by means of the proposed methodology

Game Theory for Multi-Access Edge Computing:Survey, Use Cases, and Future Trends

Game theory (GT) has been used with significant success to formulate, and either design or optimize, the operation of many representative communications and networking scenarios. The games in these scenarios involve, as usual, diverse players with conflicting goals. This paper primarily surveys the literature that has applied theoretical games to wireless networks, emphasizing use cases of upcoming multiaccess edge computing (MEC). MEC is relatively new and offers cloud services at the network periphery, aiming to reduce service latency backhaul load, and enhance relevant operational aspects such as quality of experience or security. Our presentation of GT is focused on the major challenges imposed by MEC services over the wireless resources. The survey is divided into classical and evolutionary games. Then, our discussion proceeds to more specific aspects which have a considerable impact on the game's usefulness, namely, rational versus evolving strategies, cooperation among players, available game information, the way the game is played (single turn, repeated), the game's model evaluation, and how the model results can be applied for both optimizing resource-constrained resources and balancing diverse tradeoffs in real edge networking scenarios. Finally, we reflect on lessons learned, highlighting future trends and research directions for applying theoretical model games in upcoming MEC services, considering both network design issues and usage scenarios